3) Consider an economy spanned by N risky assets and a risk free asset, where th

Question

3) Consider an economy spanned by N risky assets and a risk free asset, where the maximum Sharpe ratio is 0.56 and the risk free asset (F) yields 6%. All investors can buy or sell the following funds:

Fund

Expected Return

Standard Deviation

Select

8.5%

5%

Average

20%

25%

Aggressive

24%

35%

A client of yours who is highly risk-averse wants to invest in a fund with a standard deviation of only 5%. He has been approached by Tom Fund, the legendary fund manager that runs the “Select” fund. Should your client invest his savings in the “Select” fund? Why or why not? If not, how could he do better and still maintain a standard deviation of 5%? What expected return can he achieve?

Another client of yours wants to invest in a fund with a standard deviation of 30%. What would you recommend to her? Clearly explain in which assets she should invest in order to achieve her objective. What expected return is she going to get?

Fund

Expected Return

Standard Deviation

Select

8.5%

5%

Average

20%

25%

Aggressive

24%

35%

Explanation / Answer

Answer: Sharpe index=Rp-Rf/standard deviation

Select =8.5-6/5=0.5

Average=20-6/25=0.56

Aggressive=24-6/35=0.5142857

Ranking

Select = II

Average =I

Aggressive=III

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